The internal structure of the Fin-Ray fingers plays a significant role in their adaptability and grasping performance. However, modeling the grasp force and deformation behavior for design purposes is challenging. When the Fin-Ray finger becomes more rigid and capable of exerting higher forces, it becomes less delicate in handling objects. The contrast between these two gives rise to a multi-objective optimization problem. We employ the finite element method to estimate the deflections and contact forces of the Fin-Ray fingers grasping cylindrical objects, generating a dataset of 120 simulations. This dataset includes three input variables: the thickness of the front and support beams, the thickness of the crossbeams, and the equal spacing between the crossbeams, which are the design variables in the optimization. This dataset is then used to construct a multilayer perceptron (MLP) with four output neurons predicting the contact force and tip displacement in two directions. The magnitudes of maximum contact force and maximum tip displacement are two optimization objectives, showing the trade-off between force and delicate manipulation. The set of solutions is found using the non-dominated sorting genetic algorithm (NSGA-II). The results of the simulations demonstrate that the proposed methodology can be used to improve the design and grasping performance of soft grippers, aiding to choose a design not only for delicate grasping but also for high-force applications.